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A hosohedron is a regular tiling or map on a sphere composed of p digons or spherical lunes, all with the same two vertices and the same vertex angles, 2pi/p. Its Schläfli ...

A geodesic triangle with oriented boundary yields a curve which is piecewise differentiable. Furthermore, the tangent vector varies continuously at all but the three corner ...

The azimuthal coordinate on the surface of a sphere (theta in spherical coordinates) or on a spheroid (in prolate or oblate spheroidal coordinates). Longitude is defined such ...

The north pole is the point on a sphere with maximum z-coordinate for a given coordinate system. For a rotating sphere like the Earth, the natural coordinate system is ...

There are two different definitions of the polar angle. In the plane, the polar angle theta is the counterclockwise angle from the x-axis at which a point in the xy-plane ...

The formulas j_n(z) = z^n(-1/zd/(dz))^n(sinz)/z (1) y_n(z) = -z^n(-1/zd/(dz))^n(cosz)/z (2) for n=0, 1, 2, ..., where j_n(z) is a spherical Bessel function of the first kind ...

The south pole is the point on a sphere with minimum z-coordinate for a given coordinate system. For a rotating sphere like the Earth, the natural coordinate system is ...

An ungula is a portion of a solid of revolution obtained by cutting via a plane oblique to its base. The term derives from the Latin word ungula for the hoof of a horse. ...

In the Wolfram Language, WignerD[{j, m ,n}, psi, theta, phi] gives the m×n matrix element of a (2j+1)-dimensional unitary representation of SU(2) parametrized by three Euler ...

The solid angle Omega subtended by a surface S is defined as the surface area Omega of a unit sphere covered by the surface's projection onto the sphere. This can be written ...